More by Ivan Nourdin

Abstract

We extend, in the free probability framework, an invariance principle for multilinear homogeneous sums with low influences recently established by Mossel, O’Donnel and Oleszkiewicz in [Ann. of Math. (2) 171 (2010) 295–341]. We then deduce several universality phenomenons, in the spirit of the paper [Ann. Probab.38 (2010) 1947–1985] by Nourdin, Peccati and Reinert.